The thermonuclear explosion of a massive white dwarf in a Type Ia supernova explosion is characterized by vastly disparate spatial and temporal scales. The extreme dynamic range inherent to the problem prevents the use of direct numerical simulation and forces modelers to resort to subgrid models to describe physical processes taking place on unresolved scales. The properties of the evolution of a model thermonuclear flame in a constant gravitational field on a periodic domain are examined. The form of the governing equation of the flame surface evolution suggested by Khokhlov (1995) is confirmed. A new flame surface enhancement subgrid-scale model is developed based on this governing equation.
Another problem that relates to a Type Ia supernova explosion is the modeling and understanding of the “smoldering” phase in Type Ia supernova progenitors. A new algorithm for simulating these low Mach number inviscid flows with presence of gravity will be introduced.